The pair were returning from a trip to Barbados - where Rihanna was born and raised.
NBC News have reported that Rocky - real name Rakim Mayers - had been "under investigation" for an incident that occurred in California in November last year.
Police reports obtained by the outlet say the shooting victim told police the rapper "shot at him three to four times and believed one of the bullets grazed his left hand."
News of the arrest marks the first public reporting of the shooting.
He was later booked into jail with bail set at US$550,000, and released less than three hours later after posting bond. He's set to visit court in August.